Bifurcation Analysis of an Airfoil Containing a Cubic Structural Nonlinearity and Subjected to Two-Dimensional Incompressible Flow

Abstract

The objective of the present work is detail bifurcation analysis of an airfoil subjected to two-dimensional incompressible inviscid flow taking into account a cubic structural nonlinearity in the pitch direction. The integro-dierenti al aeroelastic equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary dierential equations. The reformulated equations are then used for the bifurcation analysis of an airfoil with a cubic structural nonlinearity in the pitch direction. The equations are either integrated numerically using defect-controlled method or analyzed using collocation method via AUTO software package. Fixed-point solutions are calculated analytically, and bifurcation diagrams showing both stable and unstable limit cycle oscillation are obtained. The types of bifurcations are assessed by evaluating the Floquet multipliers. A period doubling route to chaos was detected, and mildly chaotic behavior in a narrow range of velocity was confirmed via the calculation of the Lyapunov exponents.